Hi Helen P

As the others have said, St Kilda Road is in an excellent spot - close to city and there are lots of trams that will take you there. However, trams can be a nuisance with strollers as the old ones all have big steps to get into the tram. Now there are also lots of newer ones that are lower to the ground so not such a drama. If you're going to be taking the kids on your own, that's one thing to consider but if your DH will be with you then no big deal. There is lots of parkland close to St Kilda Road BUT not many food places after office hours. Not sure if you're planning on eating in or out.

St Kilda is also great but it gets v busy. It has a beach so very pretty but there are lots and lots of people around. Not sure how you feel about crowds. Don't worry about the prostitutes, they're not on the main streets anyway and hardly likely to hassle a woman with two kids!

Like someone else has already said, I'd recommend Melbourne Central in the city for shopping. It has a good range of shops and has a lot more character than most shopping centres. If you're staying close to the CBD, Chadstone and Southland will be way too far. DFO at the Southern Cross station is also good.